Optimisation for identifying critical emergency evacuation facilities on stochastic transportation networks

Identifying critical facilities is crucial for emergency evacuation. The r interdiction median problem (RIM) was first formulated as a mixed-integer programming model. However, it is observed that the congestion effect of transportation network cannot be just ignored during the emergency evacuation. This paper attempts to present an analytical model for identifying critical evacuation facilities involving stochastic evacuation traffic flow assignment. RIM is extend with traffic assignment techniques under a bilevel programming framework. In this model, the upper level aims at identifying critical shelters, and the lower level conveys stochastic user equilibrium problems. The model simultaneously captures the interaction between the emergency shelter interdictions and transportation network flow assignment. This model is analysed with a classical example to justify how the interdiction and traffic congestion impact the emergency evacuation and the shelter location. For solving this model, a multiagent evolutionary algorithms-based iterative approach and an augmented Lagrangian method are employed. A series of numerical example studies are conducted to test the performance of the proposed model and algorithms.